What is the sum of the arithmetic sequence that starts with 3, 9, and 15 if there are 36 terms?

To find the sum of the arithmetic sequence given the first few terms (3, 9, 15) and the total number of terms (36), we can follow a simple process. An arithmetic sequence is defined by a starting number (the first term) and a common difference between consecutive terms.

First, let’s identify the first term and the common difference:

• First term (a): The first term of the sequence is 3.
• Common difference (d): To find the common difference, we subtract the first term from the second term. So, d = 9 – 3 = 6.

Now, we can determine the n^th term of the sequence using the formula:

n^th term (a_n): an = a + (n - 1) * d

In this case, we want to find the 36^th term (a₃₆):

a36 = 3 + (36 - 1) * 6

a36 = 3 + 35 * 6

a36 = 3 + 210

a36 = 213

With the first term and the last term identified, we can now calculate the sum of the sequence using the formula for the sum of an arithmetic series:

Sum (S_n): Sn = (n / 2) * (a + an)

Substituting the known values:

S36 = (36 / 2) * (3 + 213)

S36 = 18 * 216

S36 = 3888

Thus, the sum of the arithmetic sequence consisting of 36 terms starting with 3, 9, and 15 is 3888.